3. An actual scenario using the sampling distribution of the sample proportion. It is well known...

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3. An actual scenario using the sampling distribution of the sample proportion. It is well known that the probability that a newborn is a boy is very close to 0.5. In other words, in the 'population' of newborns, the proportion of boys is p = .5. There are lots of folk-beliefs regarding what might affect whether a baby is a boy or a girl. Some people wonder, for instance, if a baby born near Christmas is more likely to be a boy. One actual set of births that might be used to test this folk belief was reported in The Sunday Mail newspaper on December 21, 1997. The article* reported on 44 babies that were born in the same 24-hour period on December 18, 1997, at the same hospital in Brisbane, Australia. *Babies By the Dozen, as described in the Journal of Statistics Education v.7, n.3 (1999); dataset available online at: http://www.amstat.org/publications/jse/secure/v7n3/datasets.dunn.cfm [Note, this is real data]. For the purpose of this exercise, we will consider these 44 babies to be a random sample from among all possible babies. According to the news article, of the 44 babies born at the hospital within the day, 26 were boys. The question is whether this (higher than expected) sample result of p = 26/44.59 could have happened just by chance (i.e., due to the sampling variability of when p = .5) or whether it is unusually high enough to provide evidence that the folk-belief that babies born near Christmas are more likely to be boys is true. In order to answer this question we need to know the sampling distribution of in this case and see which values are reasonable and which values are unusual. (a) Assuming that p = .5, what is the sampling distribution of p, the proportion of boys among 44 babies? Be sure to mention: the shape of the distribution (do not forget to justify your answer), the mean (p) and, the standard deviation (p). 3. An actual scenario using the sampling distribution of the sample proportion. It is well known that the probability that a newborn is a boy is very close to 0.5. In other words, in the 'population' of newborns, the proportion of boys is p = .5. There are lots of folk-beliefs regarding what might affect whether a baby is a boy or a girl. Some people wonder, for instance, if a baby born near Christmas is more likely to be a boy. One actual set of births that might be used to test this folk belief was reported in The Sunday Mail newspaper on December 21, 1997. The article* reported on 44 babies that were born in the same 24-hour period on December 18, 1997, at the same hospital in Brisbane, Australia. *Babies By the Dozen, as described in the Journal of Statistics Education v.7, n.3 (1999); dataset available online at: http://www.amstat.org/publications/jse/secure/v7n3/datasets.dunn.cfm [Note, this is real data]. For the purpose of this exercise, we will consider these 44 babies to be a random sample from among all possible babies. According to the news article, of the 44 babies born at the hospital within the day, 26 were boys. The question is whether this (higher than expected) sample result of p = 26/44.59 could have happened just by chance (i.e., due to the sampling variability of when p = .5) or whether it is unusually high enough to provide evidence that the folk-belief that babies born near Christmas are more likely to be boys is true. In order to answer this question we need to know the sampling distribution of in this case and see which values are reasonable and which values are unusual. (a) Assuming that p = .5, what is the sampling distribution of p, the proportion of boys among 44 babies? Be sure to mention: the shape of the distribution (do not forget to justify your answer), the mean (p) and, the standard deviation (p).